When Gen. Michael V. Hayden, former director of the National Security Agency and CIA, was running the government's largest intelligence agencies, he had to bite his tongue when the press reported on the "Big Brother" tactics in Washington and big businesses took it on the chin as a result.

Leaks from former Booz Allen Hamilton employee Edward Snowden demonstrated that a federal court granted permission to the NSA to collect all of telco giant Verizon's customer's metadata and runs an intelligence program to monitor users of America's biggest Internet companies.

In response, Google and Facebook have said they now want to tell their customers more about their relationship with the intelligence agencies even though any Foreign Intelligence Surveillance Act (FISA) court order prohibits them from doing so.

Unlike their counterparts in Silicon Valley, Verizon, the subject of the leaked FISA court order, has remained mum thus far. Revelations that the NSA was secretly collecting data from AT&T, Verizon and Bell South date back to 2006, before the massive adoption of Google and Facebook.

Appearing on CNBC's "Squawk Box" on Thursday, Hayden set the record straight about the documents leaked by a former low-level NSA contractor, Edward Snowden, and the defensive position that household-name companies and Internet high fliers find themselves in when the news breaks.

"Believe me, I feel their pain. I cannot tell you the number of times ... when the press has a story and walks it into the darkest corner of the room, there are inaccuracies, exaggerations and all I wanted to do was go public and set the record straight but I couldn't."

On the metadata side, the subject of the Verizon court order, Hayden said, "What the government has access to, what is being delivered is fundamentally billing records, created by the carriers for their own purposes and shared under a court order."

A separate NSA intelligence program revealed by Snowden last week with a PowerPoint title of "Prism," collects emails, chat room conversations and other digital data. According to Hayden, the "NSA gets to access this data for foreign intelligence purposes, not limited to terrorism, but the data NSA is asking for has to deal with foreign persons, not U.S. citizens."

Hayden called Snowden's claim he could access a U.S. president's email, "Absurd ... and it violates the law of physics."